ICTP Mathematics Seminar - Tuesday 28 February 2023, at 17:15 (Andras Nemethi)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2023


Tuesday 28 February, at 17:15 hrs.


Andras Nemethi (Hungarian Academy of Sciences)

Title: Lattice homology of curve singularities and Heegaard Floer Link 
theory

Abstract: We construct the analogue of the Heegaard Floer Link homology 
for an algebraic curve singularity, even if it is not planar, that is, 
for curve germs $(C,o)\subset ({\mathbb C}^N,o)$.
In the first step we define the lattice homology of the germ. Then, via 
a convenient filtration we define a spectral sequence, whose $E^\infty$ 
page is the graded lattice homology, while the first page $E^1$ is the 
above mentioned invariant.
If the curve singularity is in $({\mathbb C}^2,0)$ then the $E^1$ page 
can be identified  with the Heegaard Floer Link homology of the 
algebraic link in $S^3$ associated with $(C,o)$; but even in this case 
the spectral sequence is `new' (it is not the spectral sequence from 
$HFL^-$ theory which converges to $HF^-(S^3)$).
All the pages are well-defined invariants of the singularity (even if it 
is not planar).

VENUE:  Budinich Lecture Hall (ICTP Leonardo da Vinci Building)

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